A microscopic interpretation for adaptive dynamics trait substitution sequence models

Nicolas Champagnat

Stochastic Processes and their Applications, 2006, vol. 116, issue 8, 1127-1160

Abstract: We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability [mu] of mutation at each birth event. We introduce a renormalization parameter K scaling the size of the population, which leads, when K-->+[infinity], to a deterministic dynamics for the density of individuals holding a given trait. By combining in a non-standard way the limits of large population (K-->+[infinity]) and of small mutations ([mu]-->0), we prove that a timescale separation between the birth and death events and the mutation events occurs and that the interacting particle microscopic process converges for finite dimensional distributions to the biological model of evolution known as the "monomorphic trait substitution sequence" model of adaptive dynamics, which describes the Darwinian evolution in an asexual population as a Markov jump process in the trait space.

Keywords: Measure-valued; process; Interacting; particle; system; Mutation-selection; processes; Darwinian; evolution; Trait; substitution; sequence; Adaptive; dynamics; Finite; dimensional; distributions; convergence; Timescale; separation; Stochastic; domination; Branching; processes; Large; deviations (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00005-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:116:y:2006:i:8:p:1127-1160

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().